Formation Channels of Gravitationally Resolvable Double White Dwarf Binaries Inside Globular Clusters

TL;DR

The paper tackles how to identify gravitational-wave sources of double white dwarfs (DWDs) in globular clusters and distinguish them from field populations by exploiting formation channels unique to dense environments. It employs MOCCA-SURVEY globular cluster simulations with multiple stellar populations and uses LEGWORK to compute LISA-band GW signals for about $6.466 imes10^4$ DWDs, of which $3.289$ are resolvable with a threshold of $ ext{SNR}> ext{10}$ over a 5-year observation. The results show that eccentric, tight DWDs can originate only through dynamical channels, yielding an MW-wide upper limit of roughly $10$–$15$ resolvable systems and implying short merger times, typically on the order of a few Myr. This work provides a framework for using GW observations to probe dense-cluster binary evolution, and it suggests that eccentric DWDs could enable independent distance estimates to their host clusters, enhancing GW population studies and globular cluster astrophysics.

Abstract

Current gravitational wave detectors are sensitive to coalescing black holes and neutron stars. However, double white dwarfs (DWDs) have long been recognized as promising sources of gravitational waves, and upcoming detectors like LISA will be able to observe these systems in abundance. DWDs are expected to be the dominant gravitational wave (GW) sources in parts of the LISA frequency range, making it crucial to understand their formation for future detections. The Milky Way contains many white dwarfs (WDs) in both the field and star clusters, promising a rich population of DWDs for LISA. However, the large number of sources may make it difficult to resolve individual binaries, and DWDs in the field and clusters often have similar properties, complicating the identification of their origins from GW signals alone. In this work, we focus on eccentric and tight DWDs, which cannot form in the field, but require dynamical interactions in dense clusters to increase their eccentricity after circularization through mass transfer phases and common-envelope evolution during binary evolution. These binaries may also form in three- and four-body dynamical interactions where a DWD binary may directly form with high eccentricity and low separation. Our results show that we should expect eccentric and tight DWDs in clusters that can provide meaningful GW signal, however, the number is low; with an upper limit of 10-15 in the MW. These can be used to independently obtain distances of their host cluster.

Figures (5)

• Figure 1: Histograms of the binary property distributions. The blue bars represents the whole dataset (64660 binaries) while the orange bars represents the resolvable binaries (3289 binaries). Panel a) shows the semi-major axis, panel b) shows the eccentricity, panels c) and d) shows the primary and secondary mass respectively and panel e) shows the mass ratio $\left(\frac{M2}{M1}\right)$.
• Figure 2: Histograms of the resolvable binary property distributions of the three formation channels: primordial binaries that were not involved in any dynamical interaction (blue), primordial binaries that were involved in dynamical interactions (orange) and dynamically formed binaries (green). Panel a) shows the semi-major axis, panel b) shows the eccentricity in log scale to highlight outliers, panels c) and d) shows the primary and secondary mass respectively and panel e) shows the mass ratio $\left(\frac{M2}{M1}\right)$.
• Figure 3: Distribution of merger time for the resolvable DWDs in our dataset.
• Figure 4: Orbital frequency plotted against signal-to-noise ratio for our resolvable binaries at a distance of 2 kpc and 5 years observation time. The different colors are explained in Fig.\ref{['fig:binaryProperties_resolvable']}. Circles represent circular binaries, triangles represent eccentric binaries that were not involved in any dynamical interactions after the formation of the DWD. Stars represent eccentric binaries that were involved in dynamical interactions after both components had evolved into WDs. The blue points follow the same curve as the orange points but are hidden due to the large number of points.
• Figure 5: Number of resolvable eccentric binaries (blue) and upper limit of expected number of resolvable eccentric binaries in the MW (orange) against the distance to the source.